Pinch Penny is used as a noun to describe a thrifty person, meaning someone who is being frugal or stingy, or as a verb, as in 'to pinch pennies', when describing the action of saving money and not spending any.
Examples in use:
“We want to buy our own home, so we’re pinching pennies and saving as much money as we can.”
“His "pinch penny" uncle is not likely to help him pay off his student loan.”
This phrase originated in the year 1582. Nowadays, it's more common to say penny-pincher